U.S. patent number 9,513,213 [Application Number 13/962,816] was granted by the patent office on 2016-12-06 for system and method of determining rock properties using terahertz-band dielectric measurements.
This patent grant is currently assigned to SCHLUMBERGER TECHNOLOGY CORPORATION. The grantee listed for this patent is A. Ballard Andrews, Richard Averitt, Logan Chieffo, Michael M. Herron, Andrew Speck, Ronald E. G. Van Hal. Invention is credited to A. Ballard Andrews, Richard Averitt, Logan Chieffo, Michael M. Herron, Andrew Speck, Ronald E. G. Van Hal.
United States Patent |
9,513,213 |
Chieffo , et al. |
December 6, 2016 |
System and method of determining rock properties using
terahertz-band dielectric measurements
Abstract
A method of analyzing physical properties of a sample includes
obtaining the sample and obtaining an electromagnetic spectrum of
the sample using terahertz spectroscopy. A sample complex
permittivity is computed from the electromagnetic spectrum of the
sample. The method further includes estimating the constituents and
the constituent fractions and computing an estimated effective
complex permittivity based upon a model and the constituent
fractions. The method further includes comparing the computed
sample complex permittivity with the estimated effective complex
permittivity in order to determine the physical properties the
sample.
Inventors: |
Chieffo; Logan (Cambridge,
MA), Averitt; Richard (Newton, MA), Speck; Andrew
(Milton, MA), Herron; Michael M. (Cambridge, MA),
Andrews; A. Ballard (Wilton, CT), Van Hal; Ronald E. G.
(Belmont, MA) |
Applicant: |
Name |
City |
State |
Country |
Type |
Chieffo; Logan
Averitt; Richard
Speck; Andrew
Herron; Michael M.
Andrews; A. Ballard
Van Hal; Ronald E. G. |
Cambridge
Newton
Milton
Cambridge
Wilton
Belmont |
MA
MA
MA
MA
CT
MA |
US
US
US
US
US
US |
|
|
Assignee: |
SCHLUMBERGER TECHNOLOGY
CORPORATION (Sugar Land, TX)
|
Family
ID: |
52449331 |
Appl.
No.: |
13/962,816 |
Filed: |
August 8, 2013 |
Prior Publication Data
|
|
|
|
Document
Identifier |
Publication Date |
|
US 20150046090 A1 |
Feb 12, 2015 |
|
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
G01N
21/3586 (20130101); G01N 33/241 (20130101) |
Current International
Class: |
G01N
21/3586 (20140101); G01N 33/24 (20060101) |
References Cited
[Referenced By]
U.S. Patent Documents
Other References
Scales et al., Millimeter Wave Spectroscopy of Rocks and Fluids,
2006, Applied Physics Letters 88, 3 pp. cited by examiner .
Ervasti, et al., "A Study on the Resolution of a Terahertz
Spectrometer for the Assessment of the Porosity of Pharmaceutical
Tablets", Applied Spectroscopy, vol. 66 (3), 2012, pp. 319-323.
cited by applicant .
Li, et al., "Precisely optical material parameter determination by
time domain waveform rebuilding with THz time-domain spectroscopy",
Optics Communications, vol. 283, 2010, pp. 4701-4706. cited by
applicant .
O'Hara, et al., "Enhanced terahertz detection via ErAs:GaAs
nanoisland superlattices", Applied Physics Letters, vol. 88, 2006,
3 pgs. cited by applicant .
Pupeza, et al., "Highly accurate optical material parameter
determination with THz time-domain spectroscopy", Optics Express,
vol. 15 (7), Apr. 2, 2007, pp. 4335-4350. cited by applicant .
Wang, et al., "A simplified model for the dielectric function of
three-component composite materials", Physica A: Statistical
Mechanics and Its Applications, vol. 275 (1), 2000, pp. 256-261.
cited by applicant .
Young Kim, KI, "Recent Optical and Photonic Technologies",
Electrical and Electronic Engineering, 2010, pp. 231-250. cited by
applicant.
|
Primary Examiner: Le; Toan
Attorney, Agent or Firm: Matthews; Daniel S.
Claims
What is claimed is:
1. A method of analyzing a physical property of a sample, the
method comprising: operating a terahertz spectrometer to obtain an
electromagnetic spectrum of the sample, wherein the electromagnetic
spectrum comprises a terahertz spectrum; computing a sample complex
permittivity from the electromagnetic spectrum of the sample;
estimating types of constituents and constituent fractions;
computing an estimated effective complex permittivity based upon a
model and the constituent fractions; and comparing the computed
sample complex permittivity with the estimated effective complex
permittivity to determine the physical property of the sample.
2. The method of claim 1, wherein the model is determined using a
dielectric mixing law that combines known reference complex
permitivities for each of the constituents using the constituent
fractions.
3. The method of claim 2, wherein the comparing further comprises:
minimizing a difference between the estimated effective complex
permittivity and the sample complex permittivity by varying the
estimated constituent fractions; and determining the physical
property of the sample using the estimated constituent fractions
that minimize the difference between the estimated effective
complex permittivity and the sample complex permittivity.
4. The method of claim 3, wherein minimizing the difference
comprises using a nonlinear least squares fit of the sample complex
permittivity to the estimated effective complex permittivity using
at least one estimated constituent fraction as a fitting
parameter.
5. The method of claim 2, wherein one of the estimated constituent
fractions is a volume fraction of a rock matrix of the sample.
6. The method of claim 5, wherein one of the estimated constituent
fractions is selected from a group consisting of water volume
fraction, oil volume fraction, and gas volume fraction.
7. The method of claim 2, wherein one of the estimated fractions is
a volume fraction of a mineral constituent of the sample.
8. The method of claim 7, wherein the mineral constituent of the
sample is selected from a group consisting of smectite and
illite.
9. The method of claim 2, wherein one of the estimated constituent
fractions is a volume fraction of smectite and another of the
estimated fractions is a volume fraction of illite.
10. The method of claim 2, wherein an initial estimate of at least
one of the estimated fractions is obtained by Fourier transform
spectroscopy of the sample.
11. The method of claim 2, wherein the dielectric mixing law is
selected from a group consisting of a Maxwell Garnett (MG) model,
Polder and van Santen (PvS) model, Bruggeman model, and a Landau,
Lifshitz, Looyenga (LLG) model.
12. The method of claim 1, further comprising: creating the sample,
wherein the creating comprises: obtaining a raw earth sample;
crushing the raw earth sample to create a crushed earth sample;
mixing the crushed earth sample with a matrix material to create a
crushed sample-matrix mixture; and pressing the crushed
sample-matrix mixture to form the sample.
13. The method of claim 1, comprising obtaining the electromagnetic
spectrum by terahertz time domain spectrometry.
14. A system for terahertz ("THz") band dielectric measurements,
the system comprising: a THz spectrometer configured to obtain a
THz spectrum of a sample; and an analysis module configured to:
receive the THz spectrum of the sample; compute a sample complex
permittivity from the THz spectrum of the sample; estimate types of
constituents and constituent fractions; compute an estimated
effective complex permittivity based upon a model and the
constituent fractions; and compare the computed sample complex
permittivity with the estimated effective complex permittivity to
determine a physical property of the sample.
15. The system of claim 14, wherein the analysis module further
comprises: a sample modeling engine configured determine the model
of the sample using a dielectric mixing law that combines a
plurality of known reference complex permitivities for each of the
constituents using the estimated constituent fractions.
16. The system of claim 15, wherein the analysis module further
comprises: an error estimation engine configured to: minimize a
difference between the estimated effective complex permittivity and
the sample complex permittivity by varying the estimated
constituent fractions; and determine the physical properties of the
sample using the estimated constituent fractions that minimize the
difference between the estimated effective complex permittivity and
the sample complex permittivity.
17. The system of claim 15, wherein one of the estimated
constituent fractions is a volume fraction of a rock matrix of the
sample.
18. The system of claim 17, wherein one of the estimated
constituent fractions is selected from a group consisting of water
volume fraction, oil volume fraction, and gas volume fraction.
19. The system of claim 14, wherein one of the estimated
constituent fractions is a volume fraction of smectite and another
of the estimated fractions is a volume fraction of illite.
20. The system of claim 14, wherein one of the estimated
constituent fractions is a volume fraction of a mineral constituent
of the sample.
21. The system of claim 20, wherein the mineral constituent of the
sample is selected from a group consisting of smectite and
illite.
22. The system of claim 14, wherein the THz spectrometer is
configured as a THz time domain spectrometer.
23. A non-transitory computer readable medium comprising computer
readable program code embodied therein, that, when executed on a
processor, causes the processor to: receive an electromagnetic
spectrum of a sample that comprises a terahertz spectrum; compute a
sample complex permittivity from the electromagnetic spectrum of
the sample; estimate types of constituents and constituent
fractions; compute an estimated effective complex permittivity
based upon a model and the constituent fractions; and compare the
computed sample complex permittivity with the estimated effective
complex permittivity to determine a physical property the
sample.
24. The non-transitory computer readable medium of claim 23,
wherein the model is determined using a dielectric mixing law that
combines a plurality of known reference complex permitivities for
each of the constituents using the constituent fractions.
25. The non-transitory computer readable medium of claim 24,
further comprising computer readable program code embodied therein,
that, when executed on a processor, causes the processor to:
compare the computed sample complex permittivity with the estimated
effective complex permittivity by minimizing a difference between
the estimated effective complex permittivity and the sample complex
permittivity by varying the estimated constituent fractions; and
determine the physical property of the sample using the estimated
constituent fractions that minimize the difference between the
estimated effective complex permittivity and the sample complex
permittivity.
26. The non-transitory computer readable medium of claim 24,
wherein one of the estimated fractions is a volume fraction of a
rock matrix of the sample.
27. The non-transitory computer readable medium of claim 24,
further comprising computer readable program code embodied therein,
that, when executed on a processor, causes the processor to obtain
the electromagnetic spectrum of the sample using terahertz time
domain spectroscopy.
28. The non-transitory computer readable medium of claim 24,
wherein one of the estimated constituent fractions is a volume
fraction of smectite and another of the plurality of estimated
fractions is a volume fraction of illite.
29. The non-transitory computer readable medium of claim 24,
wherein one of the estimated constituent fractions is a volume
fraction of a mineral constituent of the sample.
30. The non-transitory computer readable medium of claim 29,
wherein the mineral constituent of the sample is selected from a
group consisting of smectite and illite.
Description
BACKGROUND
Measurements of the dielectric constants of materials at different
frequencies are used in many different measurement schemes. For
example, capacitance measurements at low frequencies are used to
distinguish between oil and water. In the oil and gas sectors, for
example, dielectric scanners may measure these constants at
frequencies up to 1-2 GHz to determine water volume and rock
properties. In addition, Fourier transform infrared ("FTIR")
measurements in the infrared region may be used to determine
mineralogy of core samples.
Other measurements demanding sample preparation, such as those
utilizing helium pycnometry are unable to provide accurate results
in the case of unconventional oil and gas reservoirs that possess
low permeability. Nuclear magnetic resonance (NMR) based
measurements of pore volume may be used, but are often limited by
the small pores in unconventional samples that cause fast
relaxation times in the NMR signal that are difficult to accurately
measure. Commercial measurements today are generally based on
utilizing crushed samples but these techniques both add uncertainty
due to the crushing process and also are destructive measurements
may demand extensive sample preparation.
Other techniques for identifying the mineralogy of core samples
include diffuse reflective infrared Fourier transform spectroscopy
(DRIFTS). However, due to similarity of FTIR spectrum of smectite
and illite samples, DRIFTS is unable to accurately distinguish
between these notable constituents of shale beds. Similar issues in
accurately determining the concentrations of illite and smectite
have been observed in measurements taken with X-ray diffraction
(XRD).
SUMMARY
Illustrative embodiments of the present disclosure are directed to
a method for determining rock properties using terahertz band
dielectric measurements. The method includes obtaining an unknown
sample and obtaining an electromagnetic spectrum of the unknown
sample using terahertz spectroscopy. An unknown sample complex
permittivity is computed from the electromagnetic spectrum of the
unknown sample. The method further includes estimating the
constituents and constituent fractions and computing an estimated
effective complex permittivity based upon a model and the
constituent fractions. The method further includes comparing the
computed unknown sample complex permittivity with the estimated
effective complex permittivity in order to determine the physical
properties the unknown sample.
Also, various embodiments of the present disclosure are directed to
a system for determining rock properties using terahertz band
dielectric measurements. The system includes a THz spectrometer
that may obtain a THz spectrum of an unknown sample. The system
also includes an analysis module that receives an electromagnetic
spectrum of the unknown sample. In accordance with one or more
embodiments, the electromagnetic spectrum includes a terahertz
spectrum and the analysis module may compute an unknown sample
complex permittivity from the electromagnetic spectrum of the
unknown sample. The analysis module may further estimate
constituents and constituent fractions of the unknown sample. The
analysis module may further compute an estimated effective complex
permittivity based upon a model and the constituent fractions and
compare the computed unknown sample complex permittivity with the
estimated effective complex permittivity in order to determine the
physical properties the unknown sample.
Illustrative embodiments are directed to a system of determining
rock properties using terahertz band dielectric measurements that
includes a non-transitory computer readable medium. The computer
readable medium includes computer readable program code embodied
therein, that, when executed on a processor, causes the processor
to receive an electromagnetic spectrum of an unknown sample and
compute an unknown sample complex permittivity from the
electromagnetic spectrum of the unknown sample, estimate
constituents and constituent fractions of the unknown sample,
compute an estimated effective complex permittivity based upon a
model and the constituent fractions, and compare the computed
unknown sample complex permittivity with the estimated effective
complex permittivity in order to determine the physical properties
the unknown sample.
Other aspects of the disclosure will be apparent from the following
description and the appended claims.
BRIEF DESCRIPTION OF DRAWINGS
FIG. 1 shows a system in accordance with one embodiment.
FIG. 2 shows a system in accordance with one embodiment.
FIGS. 3A-3C show examples of THz-TDS data in accordance with one or
more embodiments.
FIGS. 4A-4B show examples of frequency dependent index of
refraction measurements and frequency dependent absorption
coefficient measurements made using reference samples of known
composition, in accordance with one embodiment.
FIGS. 5A-5B show examples of frequency dependent index of
refraction and frequency dependent absorption coefficient
measurements made using reference samples of known composition, in
accordance with one embodiment.
FIG. 6 shows a flow chart for a method of preparing a rock sample
used for determining rock properties using terahertz-band
dielectric measurements in accordance with one embodiment.
FIG. 7 shows a flow chart for a method of determining rock
properties using terahertz-band dielectric measurements in
accordance with one embodiment.
FIGS. 8A-8B show examples of a numerical model plotted for
different values of the model parameters that are adjusted during
the numerical fitting routine.
FIG. 9 shows an example of a computer system that may be used to
implement the system and method in accordance with one
embodiment.
DETAILED DESCRIPTION
Dielectric constant measurements can provide information such as
specific resonances of constituent minerals and molecules, and thus
such measurements are ideal for identifying detailed sample
composition. Furthermore, trends in the collective behavior of the
measured dielectric constant as a function of frequency may reveal
information that can distinguish between distinct classes of
materials such as oil versus water or sandstone versus clays.
In general, in accordance with one or more embodiments, the present
disclosure is directed to systems and methods for the determination
of rock properties using terahertz-band dielectric measurements.
Different materials, e.g., rocks, minerals, fluids, etc., have
substantially different dielectric properties in the terahertz
(THz) frequency range (approximately 0.08 THz-10 THz). These
differing responses depend, in part, on the composition and
structure of the material. Thus, by measuring the dielectric
constant of an unknown rock sample as a function of THz frequency,
and then inverting an effective medium theory, or dielectric mixing
law, the volume fractions of the constituents of an unknown sample
may be determined. For example, in the case of an unknown sample,
e.g., a core sample, obtained from a location that includes an
unconventional oil and gas reservoir, the relative fraction of
various clays may be of great importance. In accordance with one or
more embodiments, the present disclosure is directed to a system
and method that can determine the fraction of illite and smectite
in an unconventional sample using terahertz-band dielectric
measurements. In addition, in accordance with one or more
embodiments, the present disclosure is directed to a system and
method for determining the volume fraction of crude oil, natural
gas, water, and/or rock matrix in an unknown sample using
terahertz-band dielectric measurements. In addition, the systems
and methods described herein may be used to determine the porosity
and water saturation in a low permeability, unconventional core
sample. In various embodiments, the systems and methods disclosed
herein allow for the investigation of unknown rock samples in situ,
meaning that, in one or more embodiments, the measurements do not
involve replacing the component fluids in the sample with different
components and, thus the disclosed systems and methods may be used
to determine the properties of an untreated or unmodified rock
sample, i.e., as it occurs in the field, including but not limited
to, the identification of unmodified low permeability rock that is
often present in unconventional oil and gas reservoirs.
FIG. 1 shows one example of a system for the determination of rock
properties using terahertz-band dielectric measurements. In
accordance with one or more embodiments, the system includes a
terahertz spectrometer system 103 and an analysis module 105. In
the examples that follow, for the sake of simplicity, a system
employing a THz time domain spectrometer ("THz-TDS") system is
described. However, without departing from the scope of the present
disclosure, any type of THz band spectrometer may be used
including, e.g., systems that employ continuous wave (CW) THz
sources. In one or more embodiments, the analysis module is a
module for performing numerical analysis on one or more THz-TDS
spectra obtained from the THz spectrometer system 103. The analysis
module may include hardware, software, or a combination of both.
For example, the hardware may include a computer processor (not
shown) and memory (not shown). Furthermore, in accordance with one
or more embodiments, the software and/or hardware of the analysis
module 105 may include a dielectric permittivity estimation engine
107, a sample modeling engine 109, an error determination engine
115, and a data repository 111. The numerical analysis and each of
the engines can be implemented as software instructions (e.g.,
computer readable program code) that is stored in the memory and
executed by the computer processor to perform various processes as
described herein. Furthermore, the analysis module 105 may include
one or more interfaces, e.g., interfaces 105a, 105b that may
include a user interface and/or an application programming
interface (API). In accordance with one or more embodiments, the
interfaces include functionality to receive input and transmit
output, such as to a display (not shown). For example, the input
may be a THz-TDS spectrum, or more generally a THz spectrum of any
kind, of one or more core samples and other information, e.g.,
known properties, constituents and/or known rock matrices of the
core sample.
In accordance with one or more embodiments, the THz spectrometer
system 103 is configured to obtain a terahertz time domain spectrum
("THz-TDS spectrum") of a rock sample obtained from the field,
e.g., by way of a downhole coring tool or from cuttings retrieved
during drilling. In accordance with one or more embodiments, the
analysis module 105 is configured to receive a THz-TDS spectrum and
to determine one or more properties of the rock sample based on the
THz-TDS spectrum. More precisely, the analysis module 105 includes
a dielectric permittivity estimation engine 107 that determines the
complex permittivity of the sample based on the THz-TDS spectrum.
Once the complex permittivity of the sample is determined by the
dielectric permittivity estimation engine 107, a sample modeling
engine 109 constructs a model complex permittivity based on the
measured complex permittivity. In accordance with one or more
embodiments, the model complex permittivity may be based on one or
more external input parameters related to known physical properties
of the sample that are input by a user.
The model complex permittivity may be formed from combining one or
more rock constituents by way of an effective medium theory and/or
a dielectric mixing law. More precisely, the model may be formed by
combining two or more rock types and/or fluid types (including both
oil and gas) having previously known or measured complex
permitivities that are stored in the data repository 111, which
itself may include a dielectric constant database 111a and a rock
matrix database 111b. In one or more embodiments, the data
repository 111 is any type of storage unit and/or device (e.g., a
file system, database, collection of tables, or any other storage
mechanism) for storing data. Further, the data repository 111 may
include multiple different storage units and/or devices. The
multiple different storage units and/or devices may, or may not, be
of the same type or located at the same physical site. Furthermore,
in accordance with one or more embodiments, the data repository 111
includes functionality to store one or more previously measured
frequency dependent complex permitivities for various materials
such as fluids, minerals, and rock matrix types. For example, as
shown in FIG. 1, the data repository 111 may include a dielectric
constant database 111a and a rock matrix database 111b that store
the previously measured frequency dependent complex permitivities.
In addition to being accessed from the data repository 111, the
identity and/or physical properties of one or more of the
constituents in the model may be input directly by a user if
already known e.g., through the use of previous measurements. The
use of previously known constituents may serve to increase the
speed and accuracy of the computational procedure used to determine
the model complex permittivity based on the measured complex
permittivity.
Once an initial model is constructed using data from the data
repository 111 and/or user input, an error estimation engine 115
computes the error between the model complex permittivity and the
measured complex permittivity. In accordance with one or more
embodiments, if the computed error is above a predetermined
threshold, the volume fractions of the constituents that make up
the model are adjusted and an updated model is computed by the
sample modeling engine 109. The error determination engine 115 then
recomputes the error between the updated model and the measured
complex permittivity. This iterative process of 1) update model and
2) compute error, proceeds until the computed error drops below the
predetermined threshold at which time, the error determination
engine 115 outputs the model parameters, including the constituent
identities and volume fractions of the model. In accordance with
other embodiments, the iterative process may proceed until the
model constituent values, e.g., the volume fractions, converge to
stable values. Thus, the volume fractions that lead to an accurate
estimate of the volume fractions and constituents that make up the
sample are determined numerically by way of the analysis module
105.
While FIG. 1 shows a configuration of components, other
configurations may be used without departing from the scope of the
embodiments disclosed herein. For example, various components may
be combined to create a single component. As another example, the
functionality performed by a single component may be performed by
two or more components.
FIG. 2 shows an example of a terahertz time domain spectrometer
system (THz-TDS system) that, in accordance with one or more
embodiments may be employed as the THz spectrometer system 103 in
FIG. 1. The example shown in FIG. 2 is simply one example, and one
of ordinary skill in the art having the benefit of this disclosure
will recognize that any other terahertz spectrometer may be used
that can measure dielectric constants of samples within the
terahertz frequency band (e.g., microwave based continuous-wave
sources) without departing from the scope of the present
disclosure. In this example, an oscillator 201, e.g., a pulsed
Ti:Sapphire laser, generates pulses on the order of 10 to 200 fs in
duration with a center wavelength of 750 to 840 nm and a repetition
rate of 70 to 100 MHz. The pulse train from oscillator 201 is split
into two by beam splitter 202 and directed by various mirrors into
arm 203 and arm 205 of the spectrometer. In accordance with one or
more embodiments, the power in arms 203 and 205 may be
approximately 10 mW-200 mW. The portion of the pulsed beam in arm
203 is used to pump a THz emitter 207 (e.g., a photoconductive
antenna) to generate a THz pulse that is directed to, and focused
onto, the sample 211 using, for example, a parabolic mirror 208.
The portion of the pulsed beam in arm 205 is used to gate, or
trigger, a detector 209 at a variable time that is determined by
the optical path length of the arm 205, which may be set, or
scanned by delay stage 213.
In accordance with one or more embodiments, the emitter 207
includes two gold strip-lines (not shown), separated by 10 .mu.m to
1 mm, that are patterned on a gallium arsenide (GaAs) substrate.
The femtosecond pulses from the oscillator 201 are tightly focused
in the center of the strip-lines while a bias voltage is applied
across the strip-lines. In accordance with one or more embodiments,
the bias voltage is used to accelerate photo-induced free carriers
to generate a resulting current that generates a THz pulse and may
be approximately of 50 V-1 kV. The detector 209 is configured to
receive the THz pulse after it has passed through the sample 211.
In this example, another parabolic mirror 210 is used to direct the
pulse onto the detector 209. The detector 209 operates on inverse
principles and includes a dipole antenna of length 5 to 100 .mu.m.
In one such embodiment, instead of biasing the antenna externally,
the THz pulse's electric field generates a current that is measured
and is proportional to the electric field at the specific temporal
delay. In accordance with one or more embodiments, the detector is
patterned on a custom grown substrate of erbium arsenide (ErAs)
nanoisland superlattices embedded in gallium arsenide (GaAs).
Furthermore, in accordance with one or more embodiments, the design
of the superlattices may be optimized to have a minimum carrier
lifetime. After passing through the sample 211, the femtosecond
pulses are tightly focused in the gap of the dipole antenna of
detector 209. In accordance with one or more embodiments, a lock-in
amplifier (not shown) measures the current generated in the dipole
antenna gap of the detector 209 due to the incoming THz pulse.
Furthermore, in one or more embodiments, several high resistivity
silicon hyper-hemispheres (not shown) are pressed to the back of
the substrates of emitter 207 and detector 209 in order to
efficiently couple the THz radiation into and out from the emitter
and detector antennas, respectively. The resulting THz pulses
contain frequency content from 0.1-3 THz.
FIG. 3A shows an example of a THz-TDS spectrum acquired by a
THz-TDS system in accordance with one or more embodiments of the
disclosure. More specifically, the THz-TDS spectrum is the electric
field amplitude as a function of time as measured by a THz
detector, such as detector 209, shown in FIG. 2. As such, a THz-TDS
spectrum includes both amplitude and phase information, both of
which may be obtained from the Fourier transform of the THz-TDS
spectrum. In FIG. 3A, spectrum 301 is a THz-TDS spectrum obtained
for a reference sample, e.g., a THz-TDS spectrum obtained with a
THz-TDS system having no rock sample in the path of the THz pulse.
Furthermore, spectrum 305 is a THz-TDS spectrum obtained for an
unknown sample, e.g., a THz-TDS spectrum obtained with a THz-TDS
system having an unknown rock sample in the path of the THz
pulse.
In accordance with one or more embodiments, the physical parameters
of the sample may be determined from THz spectra, e.g., spectra
similar to those shown in FIG. 3A. Furthermore, one or more
embodiments of the present disclosure are not limited to the
THz-TDS systems used as examples herein. For example, the THz
spectra may be obtained using any type of THz spectrometer
including, e.g., continuous wave (CW) microwave-based systems, or
the like. In accordance with one or more embodiments, the THz-TDS
spectra are used to estimate the complex index of refraction of the
sample n(.omega.)=n(.omega.)-i.kappa.(.omega.), where n(.omega.) is
the frequency dependent (real) refractive index of the unknown
sample, .kappa.(.omega.) is the frequency dependent extinction
coefficient of the unknown sample, and .omega.=2.pi.f, where f is
the frequency of the electromagnetic radiation interacting with the
material. Furthermore, the frequency dependent extinction
coefficient .kappa.(.omega.) can be written in terms of a frequency
dependent absorption coefficient:
.alpha.(.omega.)=2.omega..kappa.(.omega.)/c.sub.0. FIG. 3B shows
the magnitude 307 and phase 309 of the transfer function of the
unknown sample obtained by dividing the Fourier transform of the
sample scan by the Fourier transform of the reference scan. As is
described in more detail below, the real part of the transfer
function is related to .kappa.(.omega.) of the sample, while the
imaginary part of the transfer function is related to n(.omega.) of
the sample. FIG. 3C shows the index of refraction 311, i.e.,
n(.omega.) and absorption coefficient 313, i.e., .alpha.(.omega.)
as computed from the transfer function as described in more detail
below.
Furthermore, in accordance with one or more embodiments, n(.omega.)
(as plotted in FIG. 3C) may be determined numerically from a
measured THz-TDS spectrum by constructing a numerical model of the
measured THz-TDS spectrum based upon an estimated complex index of
refraction and then optimizing the estimated complex index of
refraction by minimizing the error between the estimated and
measured complex indices of refraction. In other words, the optimal
estimated complex index of refraction is found to be the estimated
complex index of refraction that produces a model THz-TDS spectrum
that most closely matches the measured spectrum. Any known method
may be used to determine the estimated complex index of refraction
from the measured sample and one example of such a procedure is
described in detail below. Once the estimated complex index of
refraction is obtained, the complex permittivity may be determined
using known relationships between the real and imaginary parts of
the complex permittivity .di-elect cons.' and .di-elect cons.'',
respectively, and the index of refraction n and absorption
coefficient .alpha.:
.function.''''.alpha..times..pi..times..times..times..function.''''
##EQU00001## where the complex permittivity {tilde over (.di-elect
cons.)}=.di-elect cons.'+i.di-elect cons.''.
Once the complex permittivity is determined, the volume fractions
of the sample constituents may be determined using an effective
medium theory and/or dielectric mixing law, as described in more
detail below. More specifically, a dielectric mixing law may be
used to combine a set of reference measurements thereby forming a
model frequency dependent complex permittivity that is then
compared to the complex permittivity determined from the THz
spectrum measurements. For example, the reference measurements may
be stored in memory, e.g., in a database such as dielectric
constant database 111a and/or rock matrix database 111b or may be
both stored in a single database. Examples of reference
measurements are shown in FIGS. 4A, 4B, 5A and 5B. The final
estimate for the volume fractions of the combination of reference
materials is the combination of reference measurements that yields
the lowest error match to the measured complex permittivity. The
type of the constituents within the sample is an example of a
physical property of the sample. Also, the final estimate of the
constituent volume fractions is another example of a physical
property of the sample. Furthermore, from the final estimates of
the volume fractions, other physical properties of the sample may
be determined, e.g., the porosity and water saturation may be
determined. As used herein, porosity .phi. is defined as
.phi.=V.sub.V/V.sub.T where V.sub.V is the void volume in the
sample and V.sub.T is the total volume of the sample. Porosity is
thus given by an estimate of the volume fraction of the rock
matrix, f.sub.matrix. Water saturation, S.sub.W, is defined as
S.sub.W=V.sub.W/V.sub.V where V.sub.W is the volume of water in the
sample. Water saturation is thus given by
S.sub.W=f.sub.water/(1-f.sub.matrix) where f.sub.water is an
estimate of the volume fraction of water in the sample.
In accordance with one or more embodiments, the complex index of
refraction of the unknown sample may be determined from the THz-TDS
spectrum as described below. With the THz-TDS spectrometer
operating in transmission mode, as shown above in reference to FIG.
2, a THz pulse that has propagated through a sample may be written
as e.sub.meas(t)=e.sub.0(t)*h(t) (3) where * denotes the
convolution operator.
In other words, the measured pulse e.sub.meas(t), measured after
passing through the sample, may be written as a convolution of the
initial pulse e.sub.0(t) with a pulse response function of the
sample given by h(t). Furthermore, the response function h(t)
depends on the material parameters of the unknown sample. Then,
according to the convolution theorem, Eq. (3) may be written in the
frequency domain as E.sub.meas(.omega.)=E.sub.0(.omega.)H(.omega.)
(4) Thus, in a manner that corresponds to the response function
h(t), the transfer function H(.omega.) depends on the material
parameters of the sample. Accordingly, Eq. (3) may be rewritten in
the form of an inverse Fourier transform
.function..times..pi..times..intg..infin..infin..times..function..omega..-
function..omega..times.eI.omega..times..times..times..times.d.omega.
##EQU00002##
In accordance with one or more embodiments, a model pulse
e.sub.m(t) may be constructed from Eq. (5) using a model transfer
function H.sub.m(.omega.) that itself depends on the model complex
refractive index
n.sub.m(.omega.)=n.sub.m(.omega.)-i.kappa..sub.m(.omega.). The
complex refractive index may then be found numerically by finding
the model refractive index n.sub.m(.omega.) that minimizes the
error between e.sub.m(t) and e.sub.meas(t). In accordance with one
or more embodiments, the error function used for the minimization
may be of the form
.times..times..function..function. ##EQU00003##
In accordance with one or more embodiments, the model pulse may be
constructed in the Fourier domain with the help of Eq. (4):
E.sub.m(.omega.)=E.sub.0(.omega.)H.sub.m(.omega.) (7) and the model
pulse may be reconstructed in the time domain using Eq. (3), or
.function..times..pi..times..intg..infin..infin..times..function..omega..-
times.eI.omega..times..times..times..times.d.omega.
##EQU00004##
There are many different ways to construct E.sub.m(.omega.) using
model material parameters without departing from the scope for the
present disclosure. For example, the discussion in Li et al.,
"Precisely [sic] optical material parameter determination by time
domain waveform rebuilding with THz time-domain spectroscopy,"
Optics Communications 283, 4701 (2010), describes one such method,
a portion of which is summarized here for convenience. As described
in Li et al., multiple Fresnel reflections from the air-sample
and/or sample-air interfaces may be taken into account for maximum
accuracy depending on the temporal length of the THz acquisition.
In accordance with one or more embodiments, the Fourier transform
of the model pulse may be written as
.function..omega..function..omega..times..function..times..times..functio-
n..times..times..times..times..times..function. ##EQU00005## where
E.sub.0(.omega.) is the Fourier transform of the initial pulse; the
propagation function P(n,x)=e.sup.-j.omega.nx/c.sup.0 models the
propagation of a pulse through a material having a complex
refractive index n and a length x; n.sub.0 is the complex
refractive index of air; n.sub.1 is the complex refractive index of
the sample; d is the thickness of the sample; and L.sub.0 is the
distance between the front surface of the sample and the detector.
Thus, the function P(n.sub.0, L.sub.0-d) models the propagation of
the pulse through the air separating the sample and the detector
and the function P(n.sub.1, d) models the propagation of the pulse
through the sample. Furthermore, the Fresnel reflection and
transmission coefficients T.sub.ij and R.sub.ij model transmission
and reflection, respectively, of a THz wave that is incident from
material i and exits into material j. For example, the reflection
coefficient at the interface of the sample and air is
R.sub.10=(n.sub.0-n.sub.1)/(n.sub.0+n.sub.1) and the transmission
coefficient at the same interface is
T.sub.10=2n.sub.1/(n.sub.1+n.sub.0). The summation term accounts
for multiple "copies" of the initial pulse that result from
multiple reflections inside the sample and is determined to be the
largest integer that satisfies the inequality:
.ltoreq..times..times..times. ##EQU00006## where t.sub.max is the
time window over which the THz-TDS spectrum is obtained.
Furthermore, Eq. (9) may be written in terms of the measured
reference pulse (i.e., the pulse that propagates through the system
with no sample present) using the propagation function P(n,x).
Thus, the propagation of the reference pulse through the length
L.sub.0 in air may be modeled as
E.sub.REF(.omega.)=E.sub.0(.omega.)P(n.sub.0,L.sub.0) (10) Thus,
using Eq. (10), Eq. (9) may be rewritten as
.function..omega..function..omega..times..function..times..times..functio-
n..times..times..times..times..times..function. ##EQU00007## For a
given choice of the complex refractive index of the sample n.sub.1,
the modeled pulse e.sub.m(t) may be reconstructed from Eq. (11)
using the inverse Fourier transform shown in Eq. (8). The initial
guess for n.sub.1(.omega.)=n.sub.1(.omega.)-i.kappa..sub.1(.omega.)
may be found a number of ways. For example, they may be chosen
using the so-called quasi analytic method (QA) (i.e., neglecting
the aforementioned multiple internal reflections within the sample)
where the measured transfer function is given simply by
.function..omega..function..omega..function..omega. ##EQU00008##
Then the initial estimates may be written as follows
.function..omega..function..function..omega..times..omega..times..times..-
kappa..function..omega..function..times..times..function..omega..function.-
.omega..times..function..omega..times..omega..times..times.
##EQU00009## The final estimates for n.sub.1(.omega.) and
.kappa..sub.1(.omega.) are then chosen as the n.sub.1(.omega.) and
.kappa..sub.1(.omega.) that minimize the error between e.sub.meas
and e.sub.m(t), e.g., according to Eq. (6). In accordance with one
or more embodiments, any known numerical algorithm may be used for
the error minimization, e.g., Nelder-Mead, or the like.
Furthermore, in accordance with one or more embodiments, any form
of error function may be used and, thus, the present disclosure is
not limited to the form used in the example above.
Furthermore, while the above example used a THz-TDS spectrum as an
example, any type of THz spectrum may be used without departing
from the scope of the present disclosure. For example tunable
continuous wave (CW) sources, e.g., those sources based on
microwave systems, scaled up in frequency, may be used to obtain a
THz spectrum. In accordance with one or more embodiments, a THz
spectrum may be obtained using a CW source by measuring the THz
power transmitted (or absorbed) through (by) the sample using a THz
power detector. Furthermore phase information may be obtained from
the power absorption spectrum using Kramers-Kronig relations. For
example, one form of Kramers-Kronig relation relates the real part
of the refractive index to the absorption coefficient .alpha.:
.function..omega..pi..times..times..intg..infin..times..alpha..function..-
OMEGA..OMEGA..omega..times..times.d.OMEGA. ##EQU00010## where is
the Cauchy principle value. Thus, using Eq. (14) the frequency
dependent refractive index (real part) may be calculated from a
measurement of the frequency dependent absorption losses of the
sample. In another example, a quadrature detection scheme may be
used to retrieve both the real (in phase) and imaginary
(quadrature) components of the THz signal so that a measurement
based on quadrature detection provides information that is
substantially similar to that obtained using TDS.
FIGS. 4A, 4B, 5A, and 5B show frequency dependent index of
refraction and frequency dependent absorption coefficient
measurements made using reference samples of known composition, in
accordance with one or more embodiments of the disclosure. Sample
measurements, such as those shown in FIGS. 4A, 4B, 5A, and 5B, are
similar to those that make up the dielectric constant database 111a
and the rock matrix database 111b used in the system of FIG. 1. In
accordance with one or more embodiments, the reference measurements
may be stored as frequency dependent absorption coefficients and
frequency dependent indices of refraction as is shown in FIGS. 4A,
4B, 5A, and 5B. Equivalently, the reference measurements may be
reparameterized in terms of the real and imaginary part of the
complex permittivity, e.g., by solving Eqs. (1) and (2) for
.di-elect cons.' and .di-elect cons.''.
In accordance with one or more embodiments, the reference samples
may be pressed into pellets using high density polyethylene (an
almost transparent material at terahertz frequencies) in order to
assure homogeneous samples with well-known path lengths. Reference
samples may include samples of known minerals and/or clays such as
quartz, calcite, illite, cheto montmorillonite, Wyoming bentonite,
smectite, or the like. In accordance with one or more embodiments,
the thickness of the pellets may range from 1 mm to 4 mm depending
on the absorption coefficient of the sample. In accordance with one
or more embodiments, pressing parameters may be 5 to 15 tons of
force using a 10 to 20 mm vacuum die held at pressure for 10 to 40
minutes. For example, the material added to the high density
polyethylene may originate from core samples of rock formations
containing unconventional oil or gas.
Further, in accordance with one or more embodiments, the unknown
sample may be a core sample with a length of approximately 1 mm
having polished ends to reduce scattering from rough surfaces. In
other embodiments, core samples, or any other type of sample
obtained in the field may be ground and pressed into pellets using
high density polyethylene in order to assure homogenous samples
with well-known path lengths. In accordance with one or more
embodiments, the thickness of the pellet (along the direction of
propagation of the THz radiation) ranges from 1 mm to 4 mm
depending on the absorption coefficient of the sample. In
accordance with one or more embodiments, pressing parameters may be
5 to 15 tons of force using a 10 to 20 vacuum die held at pressure
for 10 to 40 minutes.
FIG. 6 shows an example method for preparation of a sample for
analysis by, or use as a reference in, the system and method in
accordance with one or more embodiments. While the various blocks
in this flowchart are presented and described sequentially, one of
ordinary skill will appreciate that, in accordance with one or more
embodiments, at least a portion of the blocks may be executed in
different orders, may be combined or omitted, and at least a
portion of the blocks may be executed in parallel. In process 601,
a raw earth sample is acquired, e.g., from drill cuttings, a core
sample, or an outcrop sample. This sample may be an earth sample
having an unknown, partially known, or completely known (e.g., if
the sample is to be used as a reference sample) compositional
makeup. In process 603, if desirable, the raw sample is cleaned,
e.g., using solvent extraction or other methods, to remove drilling
mud and/or formation fluids that may include, e.g., hydrocarbons or
the like. In process 605, the cleaned sample is crushed using a
sample grinder and/or mill. In accordance with one or more
embodiments, the sample is crushed to obtain a crushed sample
having particle sizes that are less than the wavelength of the
terahertz radiation to be used for the analysis of the sample. For
example, a electromagnetic wave of frequency 1 THz has a wavelength
of about 300 microns. Thus, in accordance with one or more
embodiments, the crushed sample particle size may be less than
about 300 microns for 1 THz waves. In other embodiments, the
crushed sample particle size may be substantially less than the
wavelength of the THz wave, e.g., in a range of 1-100 microns. One
of ordinary skill having the benefit of this disclosure will
appreciate that the use of other THz wavelengths may lead to
smaller or larger particle sizes for the crushed sample and thus
the sizes disclosed herein are for example purposes. In process
607, the crushed sample is mixed with a matrix material that is
substantially transparent to THz waves, and/or has a known complex
permittivity in the THz range, e.g., powder high density
polyethylene ("HDPE"), polytetrafluoroethylene (PTFE or TEFLON),
polymethylpentene (TPX), or the like. In accordance with one or
more embodiments, the crushed sample is mixed with the matrix
material, e.g., HDPE, in a weight fraction ranging from 1:10
crushed sample to HDPE to 1:1 crushed sample to HDPE. In accordance
with one or more embodiments, the combined weight of the HDPE and
sample falls within a range of 300-700 mg. In process 609, the
crushed sample HDPE mixture may be pressed into a sample pellet.
For example, in accordance with one or more embodiments, samples in
the range of 100 mg to 500 mg may be pressed by 5 to 15 tons of
force using a 10 to 20 mm vacuum die held at pressure from 10 to 40
minutes.
The specific examples of the pellet fabrication method and the
specific parameters for length, pressure, time, disclosed above are
merely for the sake of example and are not meant to limit the scope
of the present disclosure. Furthermore, one of ordinary skill will
appreciate that the samples prepared by the above-described method
may be used as reference samples (if made with samples having known
constituents) or unknown samples used that may be later
characterized using the method and system of determining rock
properties using terahertz-band dielectric measurements in
accordance with one or more embodiments.
FIG. 7 shows a flow chart for a method of determining rock
properties using terahertz-band dielectric measurements in
accordance with one or more embodiments. While the various blocks
in this flowchart are presented and described sequentially, one of
ordinary skill will appreciate that, in accordance with one or more
embodiments, at least a portion of the blocks may be executed in
different orders, may be combined or omitted, and at least a
portion of the blocks may be executed in parallel. Furthermore, the
blocks may be performed actively or passively. For example, some
blocks may be performed using polling or be interrupt driven in
accordance with one or more embodiments. By way of an example,
determination blocks may not use a processor to process an
instruction unless an interrupt is received to signify that
condition exists in accordance with one or more embodiments. As
another example, determination blocks may be performed by checking
a data value to test whether the value is consistent with a tested
condition in accordance with one or more embodiments.
In process 701, a THz spectrum of an unknown rock sample is
obtained, e.g., a THz-TDS spectrum as described above. In
accordance with one or more embodiments, the rock sample may itself
be a core sample obtained using a coring bit or downhole core
sampling tool. In another example, the rock sample is a drill
cutting from a wellbore, which is produced by a drilling process
and brought to the surface by circulation of drilling mud. The THz
spectrum may be obtained any number of ways without departing from
the scope of the present disclosure. For example, the THz-spectrum
may be retrieved from a database of previously measured THz spectra
that are stored in a computer readable memory. In addition, the THz
spectrum may be obtained directly from a terahertz time domain
spectrometry system, or any other type of THz spectrometer, shortly
after the measurement, and/or in real time as one or more THz
measurements are made. In view of the above, the present disclosure
is not limited to any particular method for obtaining a THz
spectrum.
In process 703, the complex permittivity of the unknown sample is
determined from the obtained THz spectrum. In accordance with one
or more embodiments, the complex permittivity of the unknown sample
may be obtained in a number of different ways. For example, the
complex permittivity may be obtained using the THz spectrum and a
reference spectrum taken using the THz spectrometry system without
a sample in the system (i.e., a sample of ambient air). In
accordance with one or more embodiments, the complex permittivity
of the unknown sample is determined by first estimating the complex
permittivity and then generating a model THz spectrum based on the
estimated complex permittivity. Then the final estimate for the
estimated complex permittivity is determined by choosing the
permittivity that results in a model THz spectrum that most closely
matches the measured THz spectrum. For example one such method is
described above in reference to FIGS. 3A-3B. Determining the
closest match may involve any type of numerical optimization or
minimization routine, e.g., using a least squares technique that
minimizes the difference squared between the measured THz spectrum
and the model THz spectrum. In accordance with one or more
embodiments, for the case of the THz spectrum that is a THZ-TDS
spectrum, such an error may be quantified by the error function
.times..times..function..function. ##EQU00011## where e.sub.meas(t)
is the measured THz-TDS spectrum and e.sub.m(t) is the model
THz-TDS spectrum. The error function embodied in Eq. (15) above is
merely one example of many different forms of error functions that
may be used to find the optimal model THz-TDS spectrum.
Accordingly, any error function and any numerical method may be
used without departing from the scope of the present disclosure.
Furthermore, while the above example is set forth in the time
domain, one of ordinary skill will also appreciate that the
numerical computation may also be accomplished in the frequency
domain without departing from the scope of the present disclosure.
For example, for a CW based THz spectrometer the THz spectra may be
measured directly, in which case the error function may take the
form of
.times..times..function..omega..function..omega. ##EQU00012##
In accordance with one or more embodiments, it may actually be the
complex refractive index
n.sub.1(.omega.)=n.sub.1(.omega.)-i.kappa..sub.1(.omega.) that is
directly estimated when the model THz spectrum is determined, where
the absorption coefficient
.alpha.(.omega.)=2.omega..kappa.(.omega.)/c.sub.0. Accordingly,
once n.sub.1(.omega.) and .kappa..sub.1(.omega.) are determined,
these parameters may be converted into a complex permittivity
{tilde over (.di-elect cons.)}=.di-elect cons.'+i.di-elect cons.''
using Eqs. (1) and (2) above for the index of refraction and
absorption coefficient. Eqs. (1) and (2) are reproduced below for
convenience.
.function.''''.alpha..times..pi..times..times..times..function.''''
##EQU00013##
Accordingly, by measuring the THz spectrum of an unknown sample,
the complex permittivity {tilde over (.di-elect cons.)} of the
unknown sample is determined.
In process 705, an initial estimate of the volume fractions f.sub.i
of the constituents of the unknown sample is made. For example, in
the case of an unconventional core sample, prior measurements such
as FTIR may be used to determine the rock matrix material. In
accordance with one or more embodiments, the rock matrix material
itself may be a mixture of various clays and/or minerals and, thus,
the estimate of the volume fractions may include estimates of the
volume fraction of various rocks and minerals, e.g., quartz,
calcite, smectite, illite, cheto montmorillonite, and/or Wyoming
bentonite. In addition, initial estimates may be made as to the
volume fraction of various fluids contained within the rock matrix,
e.g., volume fractions of water, ethanolamine,
methyldiethanolamine, pyridine, ethanol, isopropanol, toluene,
xylene, hexadecane, heptane, hexane, and/or various forms of crude
oil may also be estimated in process 705.
In process 707, a model complex permittivity is determined using
the estimated volume fractions and a dielectric mixing law obtained
from an effective medium theory, such as the Maxwell-Garnett
equation:
.times..times..times..times..times. ##EQU00014## where .di-elect
cons..sub.i, .di-elect cons..sub.n, and .di-elect cons..sub.E are
the dielectric constants of the inclusion constituents, the host
constituent, and the effective medium, respectively, and f.sub.i is
the volume fraction of the given inclusion constituent defined such
that .SIGMA..sub.i=1.sup.nf.sub.i=1. Without departing from the
scope of the present disclosure, any type of model may be used to
form the effective medium, e.g., Maxwell Garnett (MG) model, Polder
and van Santen (PvS) model, Bruggeman model, and a Landau,
Lifshitz, and/or Looyenga (LLG) models may be used. Further details
regarding effective medium theories and dielectric mixing laws
generally are available in T. Ervasti et al. APPLIED SPECTROSCOPY,
66, 319-323 (2012), and, e.g., in Recent Optical and Photonic
Technologies, Ki Young Kim, ed. (2010).
In process 709, the error between the frequency dependent model
complex permittivity .di-elect cons..sub.E(.omega.) and the
frequency dependent measured complex permittivity {tilde over
(.di-elect cons.)}(.omega.) is determined. In accordance with one
or more embodiments, such an error may be quantified by an error
function
.times..times..function..omega..function..omega. ##EQU00015##
However, the error function embodied in Eq. (17) above is merely
one example of many different forms of error functions that may be
used to find the constituent volume fractions.
In process 711, the determined error between the model complex
permittivity .di-elect cons..sub.E(.omega.) and the measured
complex permittivity {tilde over (.di-elect cons.)}(.omega.) is
compared against a predetermined threshold. If the error is greater
than the threshold value, the estimated sample properties used to
generate the model, e.g., the estimated volume fractions and/or the
number and type of constituents, are updated. In accordance with
one or more embodiments, any type of numerical routine may be used
to update model and compute the error, e.g., by way of a nonlinear
least squares fitting routine, or the like.
If it is determined in process 711 that the error is below the
predetermined threshold then the set, or subset, of most recent
model parameters may output as the final estimate for the unknown
sample. In one example, the output may be stored in memory or sent
to a display device for presentation to user. Accordingly, the
constituents that make up the unknown sample and/or the volume
fractions of these constituents are determined.
FIGS. 8A-8B show examples of a numerical model plotted for
different values of the model parameters that are adjusted during
the numerical fitting routine. The dotted lines show the measured
values while the solid lines show the calculated parameters given
the porosity. As described above, the porosity .phi. is defined as
.phi.=V.sub.V/V.sub.T where V.sub.V is the void volume in the
sample and V.sub.T is the total volume of the sample. Porosity is
thus given by an estimate of the volume fraction of the rock
matrix, f.sub.matrix. The fit to the measured data that produces
the minimum error occurs at a porosity of 13.6 p.u. Note this
sample has been cleaned so that there are no hydrocarbons or water
present in it. As such, the water and oil saturations are forced to
0 in the fit.
Embodiments may be implemented on virtually any type of computing
system regardless of the platform being used. For example, the
computing system may be one or more mobile devices (e.g., laptop
computer, smart phone, personal digital assistant, tablet computer,
or other mobile device), desktop computers, servers, blades in a
server chassis, or any other type of computing device or devices
that includes at least the minimum processing power, memory, and
input and output device(s) to perform one or more embodiments. For
example, as shown in FIG. 9, the computing system 900 may include
one or more computer processor(s) 902, associated memory 904 (e.g.,
random access memory (RAM), cache memory, flash memory, etc.), one
or more storage device(s) 906 (e.g., a hard disk, an optical drive
such as a compact disk (CD) drive or digital versatile disk (DVD)
drive, a flash memory stick, etc.), and numerous other elements and
functionalities. The computer processor(s) 902 may be an integrated
circuit for processing instructions. For example, the computer
processor(s) may be one or more cores, or micro-cores of a
processor. The computing system 900 may also include one or more
input device(s) 910, such as a touchscreen, keyboard, mouse,
microphone, touchpad, electronic pen, or any other type of input
device. Further, the computing system 900 may include one or more
output device(s) 908, such as a screen (e.g., a liquid crystal
display (LCD), a plasma display, touchscreen, cathode ray tube
(CRT) monitor, projector, or other display device), a printer,
external storage, or any other output device. One or more of the
output device(s) may be the same or different from the input
device(s). The computing system 900 may be connected to a network
912 (e.g., a local area network (LAN), a wide area network (WAN)
such as the Internet, mobile network, or any other type of network)
via a network interface connection (not shown). The input and
output device(s) may be locally or remotely (e.g., via the network
912) connected to the computer processor(s) 902, memory 904, and
storage device(s) 906. Many different types of computing systems
exist, and the aforementioned input and output device(s) may take
other forms.
Software instructions in the form of computer readable program code
to perform embodiments may be stored, in whole or in part,
temporarily or permanently, on a non-transitory computer readable
medium such as a CD, DVD, storage device, a diskette, a tape, flash
memory, physical memory, or any other computer readable storage
medium. Specifically, the software instructions may correspond to
computer readable program code that when executed by a
processor(s), is configured to perform embodiments.
Further, one or more elements of the aforementioned computing
system 900 may be located at a remote location and connected to the
other elements over a network 912. Further, embodiments may be
implemented on a distributed system having a plurality of nodes,
where each portion may be located on a different node within the
distributed system. In one embodiment, the node corresponds to a
distinct computing device. Further, the node may correspond to a
computer processor with associated physical memory. The node may
correspond to a computer processor or micro-core of a computer
processor with shared memory and/or resources.
The systems and methods disclosed herein generally relate to a
method for the characterization of the dielectric response of
unknown samples, e.g., unknown unconventional core samples. It will
be appreciated that the same systems and methods may be used for
performing subsurface analysis in fields such as oilfield, mining,
water retrieval, or in any field where sample characterization is
desired. Furthermore, in accordance with one or more embodiments,
the system may be deployed as a stand-alone analytical instrument,
e.g., as a lab-based analytical instrument or as ruggedized unit
for field work, or as part of a downhole logging tool for in situ
formation characterization, e.g., as part of a wireline tool, a
logging while drilling ("LWD") tool, or a measurement while
drilling ("MWD") tool. For example, in an oilfield application, the
system and methods disclosed herein may take the form of, or be
implemented within, a downhole tool for determining the composition
of a core sample. In other embodiments, the system and methods may
be deployed uphole as an analytical instrument for analysis on any
type of unknown sample. The systems and methods disclosed herein
are not limited to the above-mentioned applications and these
applications are included herein merely as a subset of examples.
Furthermore, portions of the systems and methods may be implemented
as software, hardware, firmware, or combinations thereof.
Although the preceding description has been described herein with
reference to particular means, materials and embodiments, it is not
intended to be limited to the particulars disclosed herein; rather,
it extends to functionally equivalent structures, methods and uses,
such as are within the scope of the appended claims.
* * * * *